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Sigma model

In physics, a sigma model is a field theory that describes the field as a point particle confined to move on a fixed manifold. This manifold can be taken to be any Riemannian manifold, although it is most commonly taken to be either a Lie group or a symmetric space. The model may or may not be quantized. An example of the non-quantized version is the…

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Overview

Definition

In geometric notation

Motivations and basic interpretations

Results on various spaces

Extensions

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Map overview Semantic statistics

Sigma model

Nodes109
Edges108
Triples62
Avg. degree1.98
Density0.018349
Components1

How this topic connects Entity context

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Sigma model

Top relations

related to References · 15
Sigma model → BF02859738, Bibcode, Gell-Mann, Il Nuovo Cimento, Ketov, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Lévy, Nonlinear Sigma, S2CID, Scholarpedia, Sergei, The, Wikisource-logo
related to Example: O(n) non-linear sigma model · 12
Sigma model → Euclidean, For, Heisenberg, Kronecker, Potts, See, Taking, That, The, The Lagrangian, Then, XY
related to Interpretation as quantum mechanics · 8
Sigma model → Assembling, Delta, In, Laplacian, Phi, Taking, The, This
related to Trace notation · 8
Sigma model → Cartan, Here, In, Lagrangian, Lie, Maurer, That, The
related to Definition · 6
Sigma model → For, Lagrangian, Phi, Riemannian, The, The Lagrangian
related to overview · 5
Sigma model → Gell-Mann, Julian Schwinger, Lévy, The, Unfortunately
related to In geometric notation · 4
Sigma model → Given, Phi, The, TM
related to Motivations and basic interpretations · 2
Sigma model → Several, The
is a · 1
Sigma model → field theory that describes the field as a point particle confined to move on a fixed manifold
related to On symmetric spaces · 1
Sigma model → The

Important terminology Word statistics

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Important terminology

displaystyle model sigma phi field space form manifold metric written lie taken symmetric ij one lagrangian classical product just two

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Sigma modelis afield theory that describes the field as a point particle confined to move on a fixed manifold0.90text
Sigma modelrelated to DefinitionThe Lagrangian0.60section
Sigma modelrelated to DefinitionThe0.60section
Sigma modelrelated to DefinitionLagrangian0.60section
Sigma modelrelated to DefinitionRiemannian0.60section
Sigma modelrelated to DefinitionFor0.60section
Sigma modelrelated to DefinitionPhi0.60section
Sigma modelrelated to Example: O(n) non-linear sigma modelTaking0.60section
Sigma modelrelated to Example: O(n) non-linear sigma modelKronecker0.60section
Sigma modelrelated to Example: O(n) non-linear sigma modelEuclidean0.60section
Sigma modelrelated to Example: O(n) non-linear sigma modelThat0.60section
Sigma modelrelated to Example: O(n) non-linear sigma modelThen0.60section

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